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#72225247

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Subgroups

1570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

(6,11,14,16,15,26,17,27)(7,18,19,21)(8,22)(12,24,28,25,29,35,33,36)(13,30,31,32)(20,34);(2,4)(6,12)(7,13)(8,20)(9,23)(11,24)(14,28)(15,29)(16,25)(17,33)(18,30)(19,31)(21,32)(22,34)(26,35)(27,36);(5,6,13,24,8,16,18,33,23,14,32,36,34,26,19,29,10,15,31,35,22,27,21,28,9,17,30,25,20,11,7,12);(1,2,3,4)

Polycyclic presentation:

2^11|a^2=e,c^2=fi,d^2=g,e^2=h,f^2=ij,i^2=jk,j^2=k,c^a=cij,c^b=cf,d^b=dg,e^c=ej,f^a=fjk,f^b=fi,f^e=fk,h^c=hk,i^a=ik,i^b=ij,j^b=jk

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.5);;
gap> SetPower(coll, 3, F.6*F.9);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetPower(coll, 9, F.10*F.11);;
gap> SetPower(coll, 10, F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.11);;
gap> SetConjugate(coll, 8, 3, F.8*F.11);;
gap> SetConjugate(coll, 9, 1, F.9*F.11);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 10, 2, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);